The vagaries of drafting college-bound hockey players came back to bite the Blackhawks — and drastically help the Rangers.

Kevin Hayes, the 22-year-old Boston College forward and one of the most prized prospects coming out of college as a free agent this week, decided to spurn the team that drafted him and ink a deal with the Blueshirts.

After being taken by Chicago with the No. 24 overall pick in the 2010 draft, Hayes played out his time at BC, finishing his senior season this spring as a finalist for the Hobey Baker Award given to the top college player, putting up 65 points in 40 games, second-most in the nation.

After coming out of college, players who are still unsigned become unrestricted free agents as of Aug. 15 of that offseason.

Hayes’ deal with the Rangers is believed to be near or at the entry-level maximum, which carries a $925,000 base salary, plus bonuses. If he can factor into the NHL picture with a strong training camp, it certainly helps that the contract is salary cap-friendly, as the Rangers push themselves closer and closer to the ceiling.

Before the signing, the Rangers had approximately $1.3 million left before they hit the cap limit, which was set at a lower-than-expected $69 million just before the June draft. The Rangers’ precise salary-cap number is tough to figure without knowing who makes the team. There is competition at forward brewing among youngsters J.T. Miller, Jesper Fast and Oscar Lindberg, to mix in with depth veterans such as Matt Lombardi, Tanner Glass and Lee Stempniak.

Hayes is listed at 6-foot-4 and 216 pounds, and is said to play with a bit of an edge to his game. He was a sophomore on the 2012 Boston College national championship team with current Ranger Chris Kreider, who just re-upped with a two-year deal.

The NHL announced on Wednesday a new structure to the Draft Lottery, implemented over two years, making it even tougher for teams to tank and get the first pick.

Under the new structure, being put in place for the 2015 draft, the team that finishes last in regular-season points will have a 20-percent chance at getting the first pick, as opposed to the previous 25-percent chance. Teams that finished second- to fifth-worst now have better odds at winning the first pick, and the rest of the 14 non-playoff clubs have a lower chance than they previously did at the pick.

For the following year, 2016, the same weighted lottery system will be implemented for the first three picks, meaning that the team that finishes last in the league can no longer be guaranteed to get no worse than the second pick, but can fall as low as the fourth-overall selection.